We have a pretty good timeline of the night. I will attempt to map it with known times, and suspected times.
11:55 pm - Harry and Hermione go back in time exactly 3 hours.
“I am going to lock you in. It is —” he consulted his watch, “five
minutes to midnight. Miss Granger, three turns should do it. Good
“We’ve gone back in time,” Hermione whispered, lifting the
chain off Harry’s neck in the darkness. “Three hours back . . .”
8:55 pm - Harry, Ron, and Hermione head out to Hagrids house.
“Footsteps across the hall . . . yes, I think it’s us going down to
“Are you telling me,” Harry whispered, “that we’re here in this
cupboard and we’re out there too?”
Here I'm adding a suspected time, based on sundown times for Scotland, I picked a northern area of Scotland to correspond with Hogwarts location give or take a few minutes.
10:00 pm - sundown Buckbeak's rescue
As Fudge’s voice started again, Harry darted out from behind his
tree, vaulted the fence into the pumpkin patch, and approached
“It is the decision of the Committee for the Disposal of Dangerous
Creatures that the hippogriff Buckbeak, hereafter called the con-
demned, shall be executed on the sixth of June at sundown —”
In the forest after grabbing buckbeak-
She looked nervously over her shoulder into the depths of the
forest. The sun was setting now. ...
Shortly after watching Ron get dragged under the Womping Willow.
They moved around the edge of the forest, darkness falling
thickly around them, until they were hidden behind a clump of
trees through which they could make out the Willow.
Here we have a break while the events inside the house happen. This next bit gets a little tricky, but we have some wiggle room due to the general usesage of the phrase "sundown" but it appears the events inside the house take over an hour.
Hermione sat with her face turned toward the Willow, waiting.
And then, at last, after over an hour . . .
“Here we come!” Hermione whispered.
which would bring us to
Harry, and company exit the Willow and begin the trek back up to the school. Sirius tells Harry he can live with him, Harry becomes excited, Lupin turns into a werewolf, a chase ensues, Harry runs to help Sirius at the lake, Dementors show up, Harry passes out.
11:10 pm Harry and Hermione have finished witnessing the Dementor attack, Snape starts to take them back to the castle, and they head to save Sirius with Buckbeak.
“Right, it’s nearly time,” said Hermione tensely, looking at her
watch. “We’ve got about forty-five minutes until Dumbledore
locks the door to the hospital wing. We’ve got to rescue Sirius and
get back into the ward before anybody realizes we’re missing. . . .”
The time gets a little muddied between Hagrid’s house, sundown, and them exiting the Womping Willow, But I think we can safely say that they entered the Willow within a few minutes either side of "official" sundown. A few minutes prior say 9:50-ish, would fit with the statement "over an hour later" they emerged, at 10:55-11:00, giving them 10-15 or so minutes of walking back to school, learning about staying with Sirius, running from the werewolf, and going unconscious. Before Hermione's final timestamp of 11:10.
Giving Harry a grand total of about 10-15 conscious minutes believing he could stay with Sirius, and about an hour between the time he learns of it, till he wakes up and realizes Sirius is captured, presumably crushing his hope.